# Write a polynomial function in standard form

## Multivariable polynomials in standard form

Putting this information together with the Leading Coefficient Test we can determine the end behavior of the graph of our given polynomial: Since the degree of the polynomial, 3, is odd and the leading coefficient, 5, is positive, then the graph of the given polynomial falls to the left and rises to the right. On the other hand, whenever we have that The last expression is in the standard form of a polynomial, and for most purposes one can brush over the fact that is not defined when. First question is what is the leading term? Throughout let be defined as in. If n is even AND the leading coefficient , is negative, the graph falls to the left and to the right. In polynomials with one indeterminate, the terms are usually ordered according to degree, either in "descending powers of x", with the term of largest degree first, or in "ascending powers of x". The zero polynomial is homogeneous, and, as homogeneous polynomial, its degree is undefined. Don't get distracted by the subtlety of some of these examples. If you said 3, you are right on!! For higher degrees the specific names are not commonly used, although quartic polynomial for degree four and quintic polynomial for degree five are sometimes used. A polynomial of degree zero is a constant polynomial or simply a constant. The term "quadrinomial" is occasionally used for a four-term polynomial.

Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. The argument of the polynomial is not necessarily so restricted, for instance the s-plane variable in Laplace transforms.

The term "quadrinomial" is occasionally used for a four-term polynomial.

There is no obvious way to convert it to standard form but there might be a non-obvious way that we aren't able to see. If you said 3, you are right on!! Putting this information together with the Leading Coefficient Test we can determine the end behavior of the graph of our given polynomial: Since the degree of the polynomial, 3, is odd and the leading coefficient, 5, is positive, then the graph of the given polynomial falls to the left and rises to the right.

Throughout let be defined as in. If you said -7, pat yourself on the back!! Example 4: Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial. To show that appearances may be deceiving note that is in fact a polynomial.

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